We are 3-partners company already started a year ago. We all have full time job and are working in part time to build our business idea. It is a web project and we outsource the design and development work to India. The project idea is great, but since we are working in part time, the progress is pretty slow, not only the development side, but also the marketing, the decision making, the business planning, etc. Recently, we also find that the budget is almost close to our limit. I know there are some missing pieces which needs to be completed before launch, but we have some argument about our working capital. With that in mind,

1. Should we launch our project no matter what?
2. Should we give up our idea since we don't have time to work on?
3. What other alternatives do we have?

Sorry, I can't help with any advice but this is the problem with partnerships. You might all be working from the same hymn sheet at the onset but, give it time, and I reckon most partnerships are destined to failure due to disagreements, big or small.

Obviously without knowing any details, I would personally opt for 3. and go it alone.

This is tough. It is great to have partners, but someone needs to take the lead roles in your project. What roles have you established?_________________Raise Capital in 90 Days Online!
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Sorry to be harsh, but if you don't have a solid written agreement in place and you aren't all clear on your roles and responsibilities then it's not working. The longer you drag it out the worse it will be.

OTOH, if you can all sit down, clear the air, allocate jobs and elect one person to lead the team then you may have a chance.

there's a problem in that all of you still have pt jobs
on that basis you'd struggle to get anyone to invest through this perceived lack of commitment. Which is presumably what you need if you're close to the budget and still at the idea stage.

It seems very good that you all three partners and started a business . As you said that you all are busy with your job. But one should give full time efforts in that. Otherwise you wont be able to achieve your targets.

And if anyone of you cant give full time to your business then its better to give up the idea.